[comicjk]

I dispute whether a wavefunction can influence things without collapsing, but putting that aside...

Your example of a polygon with a constant velocity is carefully chosen: that equation has an analytical solution, so you can calculate x(t) and "skip" forward in time. This is not possible in general, even in classical mechanics. If it were a system of more than two interacting particles, you wouldn't be able to fast-forward; you would have to calculate all the intermediate timesteps even if you only wanted the last one.

[EGreg]

That's only because as a human being you deal with closed form solutions.

Who is to say that the "universe simulator" is only doing 21st century math?

[comicjk]

If the universe simulator can solve iterative problems in O(1), then I question whether our concept of optimization is meaningful enough to it for this discussion to make sense.

[bicubic]

This is a very interesting question. What if the universe is stateless and any state at time T can be calculated in O(1)

What if we just lack the expressiveness or the initial conditions to model a stateless universe?

A fun consequence of stateless universe would be that you can rewind, fast forward, loop, speed up, slow down time at no extra cost.

[comicjk]

There are some physical systems (mathematically, "Hamiltonians") which have this "stateless" property. However, if the time/energy uncertainty principle is true, simulating time T in O(1) cannot be possible in general unless BQP=PSPACE (the unlikely idea that quantum computers can efficiently solve any problem that can be stored in polynomial amounts of memory). See this paper: https://arxiv.org/abs/1610.09619